patA1147
比較簡單的一道題。只要對heap有一點了解就ok。
在求後序遍歷，本來想要建樹，但後來覺得代碼太多，然後發現直接dfs就ok了。
In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))
Your job is to tell if a given complete binary tree is a heap.
Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 100), the number of trees to be tested; and N (1 < N ≤ 1,000), the number of keys in each tree, respectively. Then M lines follow, each contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.
Output Specification:
For each given tree, print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all. Then in the next line print the trees postorder traversal sequence. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line.
Sample Input:
3 8
98 72 86 60 65 12 23 50
8 38 25 58 52 82 70 60
10 28 15 12 34 9 8 56
Sample Output:
Max Heap
50 60 65 72 12 23 86 98
Min Heap
60 58 52 38 82 70 25 8
Not Heap
56 12 34 28 9 8 15 10
代碼：
#include <cstdio>
#include <vector>
using namespace std;
vector<int> levelOrder;
vector<int> postOrder;
void dfs(int start, int m) {
if(start > m) {
return;
}
dfs(start * 2, m);
dfs(start * 2 + 1, m);
postOrder.push_back(levelOrder[start]);
}
int judge(int m) {
bool mark;
bool flag = true;
int len = levelOrder.size() - 1;
if(levelOrder[1] <= levelOrder[2]) {
mark = false;
}
else {
mark = true;
}
for(int i = 1; i <= len / 2; i++) {
if(mark == false) {
if(i * 2 <= m && levelOrder[i] > levelOrder[i * 2]) {
flag = false;
break;
}
if(i * 2 + 1 <= m && levelOrder[i] > levelOrder[i * 2 + 1]) {
flag = false;
break;
}
}
else if(mark == true) {
if(i * 2 <= m && levelOrder[i] < levelOrder[i * 2]) {
flag = false;
break;
}
if(i * 2 + 1 <= m && levelOrder[i] < levelOrder[i * 2 + 1]) {
flag = false;
break;
}
}
}
if(flag == true && mark == false) {
return 2;
}
if(flag == true && mark == true) {
return 1;
}
else {
return 3;
}
}
int main() {
int n, m;
scanf("%d %d", &n, &m);
levelOrder.resize(m + 1);
for(int i = 0; i < n; i++) {
postOrder.clear();
for(int j = 1; j <= m; j++) {
scanf("%d", &levelOrder[j]);
}
int ans = judge(m);
dfs(1, m);
if(ans == 1) {
printf("Max Heap
");
}
else if(ans == 2) {
printf("Min Heap
");
}
else {
printf("Not Heap
");
}
for(int j = 0; j < m; j++) {
printf("%d", postOrder[j]);
if(j != m - 1) {
printf(" ");
}
if(j == m - 1) {
printf("
");
}
}
}
return 0;
}
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